integral of sqrt(x-1)/x dx⚡ u-substitution integral with square root скачать в хорошем качестве

integral of sqrt(x-1)/x dx⚡ u-substitution integral with square root

Solve the challenging integral ∫ √(x-1)/x dx step by step using substitution. This tutorial demonstrates the powerful technique of setting u = √(x-1) (or u² = x-1) to eliminate the radical, followed by algebraic manipulation using polynomial division. Learn how this substitution naturally leads to an inverse tangent (arctan) function. Perfect for Calculus 2 students. Final answer: 2√(x-1) - 2arctan(√(x-1)) + C. Learn to integrate √(x-1)/x using the substitution u² = x-1. This video breaks down the algebraic steps to transform the radical integral into a rational function, revealing the arctan pattern. Essential technique for integration involving roots and rational functions. Master the integration of √(x-1)/x dx with this detailed walkthrough. Discover why substituting u = √(x-1) is more effective than u = x-1, learn to manipulate the resulting rational function 2u²/(u²+1), and arrive at the solution 2√(x-1) - 2arctan(√(x-1)) + C. Includes verification tips. Unlock ∫ √(x-1)/x dx with simple u-substitution! ⚡ Perfect Calc 2 tutorial for radicals over x. integral of sqrt(x-1)/x dx how to integrate sqrt(x-1) over x integration of sqrt(x-1) divided by x solve ∫ sqrt(x-1)/x dx substitution method for sqrt(x-1)/x u-substitution integral with square root sqrt(x-1)/x antiderivative int sqrt(x-1)/x solution integration using u = sqrt(x-1) substitution trig substitution for sqrt(x-1)/x integral with algebraic manipulation and substitution step by step integral sqrt(x-1)/x integration techniques for radical over x rewrite sqrt(x-1)/x before substituting integral leading to 2 sqrt(x-1) - 2 arctan(sqrt(x-1)) + C calculus 2 integral with u-substitution and trig example of substitution u^2 = x-1 substitution u = sqrt(x-1) integration integral of sqrt(x-a)/x type integration by substitution with rational and radical Integration by parts    • Integration by parts   Trigonometric Integrals    • Trigonometric Integrals   Integration by substitution    • Integration by substitution   integral exponential functions    • THE INTEGRATION OF EXPONENTIAL FUNCTIONS   definite integrals    • definite integrals   integration by partial fractions    • integration by partial fractions   Double Integration Examples and Solutions    • double integration method   Triple Integration Examples and Solutions    • Triple Integration   Music: Local Elevator by Kevin MacLeod Free music licensed under Creative Commons: Attribution 4.0 License https://creativecommons.org/licenses/... Source: https://incompetech.com